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Date November 2017 Marks available 2 Reference code 17N.2.sl.TZ0.2
Level SL only Paper 2 Time zone TZ0
Command term Write down Question number 2 Adapted from N/A

Question

Let \(f(x) = \frac{{6{x^2} - 4}}{{{{\text{e}}^x}}}\), for \(0 \leqslant x \leqslant 7\).

Find the \(x\)-intercept of the graph of \(f\).

[2]
a.

The graph of \(f\) has a maximum at the point A. Write down the coordinates of A.

[2]
b.

On the following grid, sketch the graph of \(f\).

N17/5/MATME/SP2/ENG/TZ0/02.c

[3]
c.

Markscheme

valid approach     (M1)

eg\(\,\,\,\,\,\)\(f(x) = 0,{\text{ }} \pm 0.816\)

0.816496

\(x = \sqrt {\frac{2}{3}} \) (exact), 0.816     A1     N2

[2 marks]

a.

\((2.29099,{\text{ }}2.78124)\)

\({\text{A}}(2.29,{\text{ }}2.78)\)     A1A1     N2

[2 marks]

b.

N17/5/MATME/SP2/ENG/TZ0/02.c/M     A1A1A1     N3

 

Notes:     Award A1 for correct domain and endpoints at \(x = 0\) and \(x = 7\) in circles,

A1 for maximum in square,

A1 for approximately correct shape that passes through their \(x\)-intercept in circle and has changed from concave down to concave up between 2.29 and 7.

 

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2 - Functions and equations » 2.2 » The graph of a function; its equation \(y = f\left( x \right)\) .
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